Additivity of Dimension & Height

This lecture covers the concept of additivity of dimension and height in a finitely generated k-algebra domain. It explains the relationship between the dimension of a ring, the dimension of its prime ideal, and the height of the prime ideal. The lecture also discusses examples and applications of the additivity property, illustrating how it can be used to compute the height of prime ideals. Additionally, it explores the implications of the additivity property when the ring is finitely generated. The instructor demonstrates the additivity property through various calculations and proofs, emphasizing its significance in algebraic geometry.